A SUBGRADIENT METHODS FOR NON-SMOOTH VECTOR OPTIMIZATION PROBLEMS

Abstract

Vector optimization problems are a significant extension of scalar optimization and have wide range of application in various fields of economics, decision theory, game theory, information theory and optimal control theory. In this paper, unlike general subgradient methods, bundle methods and gradient sampling methods used to solve nonsmooth vector optimization problems which include scalarization approach, a subgradient method without usual scalariza- tion approached is proposed for minimizing a non-differentiable convex func- tion which works directly with vector-valued function. A general sub-gradient method for non-smooth convex optimization that includes regularization and interior point variants of Newton's Method are proposed. This algorithm builds a sequence of efficient points at the interior of epigraph of objective function which satisfies KKT conditions. In this paper, under the suitable conditions it is proved that the sequence generated by algorithm converges to ǫ-efficient point.